Theorems · Definition · field theory
Polynomial.leadingCoeff
{R : Type u} → [inst : Semiring R] → Polynomial R → RleadingCoeff p gives the coefficient of the highest power of X in p.
- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 498 results in Mathlib
- Foundations
- Depth 60 from the axioms, rests on 952 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
Cited by511
Results whose statement or proof uses this declaration.
- Polynomial.Monicproof · cited by 461
- Polynomial.Monic.leadingCoeffstatement · cited by 101
- Polynomial.leadingCoeff_eq_zerostatement and proof · cited by 55
- Polynomial.Monic.mapproof · cited by 52
- Polynomial.leadingCoeff_Cstatement · cited by 39
- Polynomial.leadingCoeff_ne_zerostatement and proof · cited by 39
- Polynomial.leadingCoeff_mulstatement and proof · cited by 32
- Polynomial.integralNormalizationproof · cited by 24
- Polynomial.monic_mul_leadingCoeff_invstatement and proof · cited by 19
- Polynomial.natDegree_mul'statement and proof · cited by 18
- RatFunc.num_div_denomproof · cited by 18
- Polynomial.Monic.defstatement · cited by 18
Showing the 200 most cited of 511.